Hexagon Tiles: Like them, love them, or RAGGGEEEE!!!
- Thread starter Jakerg23
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mjs0
The 4th X
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frekk
Scourge of St. Lawrence
What exactly are you pointing at?
Not sure I see what you're spotting. In my mind, if it's good enough as a standard for use in professional GIS systems that need a discrete grid system, it's definately good enough for a game.
Not sure I see what you're spotting. In my mind, if it's good enough as a standard for use in professional GIS systems that need a discrete grid system, it's definately good enough for a game.
Minor Annoyance
Deity
A pentagon in the hexagon map.
frekk
Scourge of St. Lawrence
Oh, on the big grid. Yes. There are a few of them, not sure how many exactly. I think 1 in 6 of the largest grid have to be pentagons to get it to tesselate properly.
But it's a higher grid - it might be present in the code that models the globe, but it wouldn't be part of the tileset, and you wouldn't have to see it. As you can see there are no pentagons in the lower scale grids. That's the whole trick to the technique, is using different scales of grids. Once you've got that highest tesselation done, the lower grids will tesselate onto it with only a little distortion in terms of the size of the tiles (not their shape).
There is one little detail, but its not much of a problem - it can't be fully flattened out, or it ends up looking quite strange. It's an icosahedron that's been rounded out, so if you flatten it, the sides are all over the place. In any view, there would have to be some curvature, but it would be quite minimal at the lower scales of view, unless the map was really small. There would, in fact, be a lower limit to the size of maps as well.
No problem, use traditional flat view for up close and switch to the icosahedron of Greatness when you zoom out.
Trias
Donkey with three behinds
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In the center of each pentagon there is...
...another pentagon.
You really cannot argue with Euler here.
frekk
Scourge of St. Lawrence
Who cares? The second picture is no more the final product than the first. I don't give a hoot what it looks like during development or in some deep layer of code ... the only thing that matters is the final product, and it looks to me like it's ironed out in the third and final pics. I don't see any (visible) pentagons there.
Trias
Donkey with three behinds
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Then you need to look more closely. In the third picture there is a pentagon just of the coast of Florida.
The fourth picture is just zoomed in on the area in the third one that contain no pentagons.
frekk
Scourge of St. Lawrence
Ah, seems you are right. Oh well - 1 in 100 tiles or so would be a pentagon, if you really HAD to have polar regions tiled on a globe.
Can't get around it with squares, either - there will be distortions in size depending on latitude, if the polar regions get gridded, such that if you have nice squares round the equator, things will get more and more rectangular as you move further away from it.
Can't get around it with squares, either - there will be distortions in size depending on latitude, if the polar regions get gridded, such that if you have nice squares round the equator, things will get more and more rectangular as you move further away from it.
frekk
Scourge of St. Lawrence
Ah, seems you are right. Oh well - 1 in every few hundred tiles or so would be a pentagon, if you really HAD to have polar regions tiled on a globe.
Can't get around it with squares, either - there will be distortions in size depending on latitude, if the polar regions get gridded, such that if you have nice squares round the equator, things will get more and more rectangular as you move further away from it. This would probably be much more striking than 2-3 pentagons per continent.
Can't get around it with squares, either - there will be distortions in size depending on latitude, if the polar regions get gridded, such that if you have nice squares round the equator, things will get more and more rectangular as you move further away from it. This would probably be much more striking than 2-3 pentagons per continent.
Trias
Donkey with three behinds
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Not necessarily. You can the method used in the link to project a dodecahedron subdivided in hexagon and pentagons onto a sphere, also to project a cube subdivided by squares. You will get a tiling of the sphere by 4 sided tiles, which you can get to have equal areas as well. The tiling will however have 8 special vertices (corresponding to the corners of the cube) where 3 instead of 4 tiles. Moreover tiles around these points will be significantly deformed.
Why tiles and movement has to be strongly related?
Tiles are needed for resource placement and for culture/borders.
Movements should be more linked to terrain features, natural and artificial (roads).
My vote is for hexagons an pentagons with impassable geographical features to cover the 12 pentagons (well 10 + the two poles) and spherical coordinates for movement.
BTW even in CIV IV cities and terrain improvements are not neatly packaged in squares.
Tiles are needed for resource placement and for culture/borders.
Movements should be more linked to terrain features, natural and artificial (roads).
My vote is for hexagons an pentagons with impassable geographical features to cover the 12 pentagons (well 10 + the two poles) and spherical coordinates for movement.
BTW even in CIV IV cities and terrain improvements are not neatly packaged in squares.
snapple232
Warlord
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A spherical globe map would be "cool" no doubt, but it seems like a technically challenging and complicated thing to code in, with few benefits.
Sure it allows you to have poles, but they haven't exactly played a significant role in human history, and haven't even been traversable until the last century or two.
And then there's the whole pentagon thing everybody has mentioned. As I understand it (correct me if I'm wrong), the pentagons need to be evenly spaced out across the sphere.
So the idea of putting impassable geographical features seems like it'd be very contrived, with mountains or something placed on exact, evenly spaced locations on every single map. You'd also have to deal with the fact that random ocean tiles and the two poles will inexplicably be pentagons for no apparent reason to the player.
I'm not necessarily saying that having a real sphere is a bad idea, but with no tangible benefit to gameplay as I can see it, it seems like their resources are better spent elsewhere.
Sure it allows you to have poles, but they haven't exactly played a significant role in human history, and haven't even been traversable until the last century or two.
And then there's the whole pentagon thing everybody has mentioned. As I understand it (correct me if I'm wrong), the pentagons need to be evenly spaced out across the sphere.
So the idea of putting impassable geographical features seems like it'd be very contrived, with mountains or something placed on exact, evenly spaced locations on every single map. You'd also have to deal with the fact that random ocean tiles and the two poles will inexplicably be pentagons for no apparent reason to the player.
I'm not necessarily saying that having a real sphere is a bad idea, but with no tangible benefit to gameplay as I can see it, it seems like their resources are better spent elsewhere.
Jerrymander
Epistemologist
Just make the globe a timecube.
And go to town.
And go to town.
For your viewing pleasure. http://en.wikipedia.org/wiki/Truncated_icosahedron
Hexes are FAR better, and should have been done long ago. Cid's got a great game in Civ but as I've said before, many of his ideas for the game's mechanics are just ludicrous to me - squares being one of them.
Hexes are FAR better, and should have been done long ago. Cid's got a great game in Civ but as I've said before, many of his ideas for the game's mechanics are just ludicrous to me - squares being one of them.
Hi, I am the president of the PYXIS innovation and the inventor of the indexing used on the ISEA hexagonal tessellation that you are discussing on this thread. I thought I might be able to help you out.
We call the entire mechanism a digital Earth reference model (DERM) as it encompasses the principals of a digital as opposed to an analogue way of encoding information - think of the way a sound signal (music) is encoded digitally as opposed to analog and you will mostly get the difference between the DERM and conventional coordinate systems used to reference the Earth like lat and long. Of course gamers have been well aware of the difference between such things for many years and much of the original ideas for PYXIS goes back to my own gaming days in the 70's.
So our first job was to select an optimized discretization strategy - tiling - of the Earth surface. Hexagons are generally best under most criteria however they do not aggregate and decompose congruently - like squares and triangles can - into self similiar parts. How does one create a hierarchical multi-resolution hexagonal mesh? Further studies have suggested that the ideal criteria for a Earth tilling would have each cell the same area. This is also a challenge and you have discovered that its impossible to cover the Earth with the same tile and preserve both shape and area over 20 cells - this is why there are so many patents for golf balls.
We adopted a solution called the Snyder Equal Area Icosahedral Aperture 3 Hexagonal grid (ISEA3H) first proposed by some researchers at Oregon State University who were looking at sampling for biodiversity analysis. This is a base 3 system where the grid changes by a square root three distance between cells each resolution. The area is preserved in each cell - not a meaningful trait for gaming but essential in an discrete Earth reference where statistically valid sampling of information should be preserved at any point on the planet. As noticed the exception is the 12 pentagons that will form at the vertices of the icosahedron - these are strategically placed in large water bodies for the most part - at any rate they are really really tiny for most any application - though we do have to heed them heuristically.
The indexing (addressing), mathematics (from neighbour operations to advanced algebra) and quantization strategy (sampling) are all developed and available for the grid in our library. The core value being that real time data can be synchronized to the grid and therefor multi-source analysis of Earth observations is enabled without need for a manual preprocessing typical of digital cartography and GIS. I good application for this is Geospatial-Intelligence where spatial data is brought together on the fly.
I think that if one thinks of gaming as a simulation and one uses real data to feed into that simulation, there may be some value for a game. Its rather high fidelity for a game I would expect.
If you want to look at the DERM in more detail take the following steps:
1. Down load the prototype browser on our web site - worldview - https://www.pyxisinnovation.com/downloads.php
2. Click off the 2 default data sets
3. Activate the navigation pane by picking on it - then select the numbers 0, 2 and 4 on your key pad - this will show 4 resolutions of the ISEA3H grid - it is skipping intermediate resolutions. The entire grid is pretty dense.
4. At the bottom left there is an indicator of lat long, change this to PYXIS indexing. This will show you the index of each cell at the display resolution. Note that the display resolution is tiny - smaller than the pixels on your monitor - so you won't see them. There are 265 cells in the smallest grey cells you see on the screen.
5. Use your scroll button or +- buttons to zoom in. At resolution 40 the cells are 2 mm apart.
6. You can populate the cells with almost any conventional georeferenced imagery, vectors or terrain. Just drop the file from your windows exporer into the library on the left of the screen. Its a P2P system so you can also publish your data to others.
If there is anyone interested in further information I suggest contacting us at our office 1-877-389-6619 or see website and I can have one of our engineers provide you with more.
Hope that helps out and appreciate your interest.
Regards, Perry
We call the entire mechanism a digital Earth reference model (DERM) as it encompasses the principals of a digital as opposed to an analogue way of encoding information - think of the way a sound signal (music) is encoded digitally as opposed to analog and you will mostly get the difference between the DERM and conventional coordinate systems used to reference the Earth like lat and long. Of course gamers have been well aware of the difference between such things for many years and much of the original ideas for PYXIS goes back to my own gaming days in the 70's.
So our first job was to select an optimized discretization strategy - tiling - of the Earth surface. Hexagons are generally best under most criteria however they do not aggregate and decompose congruently - like squares and triangles can - into self similiar parts. How does one create a hierarchical multi-resolution hexagonal mesh? Further studies have suggested that the ideal criteria for a Earth tilling would have each cell the same area. This is also a challenge and you have discovered that its impossible to cover the Earth with the same tile and preserve both shape and area over 20 cells - this is why there are so many patents for golf balls.
We adopted a solution called the Snyder Equal Area Icosahedral Aperture 3 Hexagonal grid (ISEA3H) first proposed by some researchers at Oregon State University who were looking at sampling for biodiversity analysis. This is a base 3 system where the grid changes by a square root three distance between cells each resolution. The area is preserved in each cell - not a meaningful trait for gaming but essential in an discrete Earth reference where statistically valid sampling of information should be preserved at any point on the planet. As noticed the exception is the 12 pentagons that will form at the vertices of the icosahedron - these are strategically placed in large water bodies for the most part - at any rate they are really really tiny for most any application - though we do have to heed them heuristically.
The indexing (addressing), mathematics (from neighbour operations to advanced algebra) and quantization strategy (sampling) are all developed and available for the grid in our library. The core value being that real time data can be synchronized to the grid and therefor multi-source analysis of Earth observations is enabled without need for a manual preprocessing typical of digital cartography and GIS. I good application for this is Geospatial-Intelligence where spatial data is brought together on the fly.
I think that if one thinks of gaming as a simulation and one uses real data to feed into that simulation, there may be some value for a game. Its rather high fidelity for a game I would expect.
If you want to look at the DERM in more detail take the following steps:
1. Down load the prototype browser on our web site - worldview - https://www.pyxisinnovation.com/downloads.php
2. Click off the 2 default data sets
3. Activate the navigation pane by picking on it - then select the numbers 0, 2 and 4 on your key pad - this will show 4 resolutions of the ISEA3H grid - it is skipping intermediate resolutions. The entire grid is pretty dense.
4. At the bottom left there is an indicator of lat long, change this to PYXIS indexing. This will show you the index of each cell at the display resolution. Note that the display resolution is tiny - smaller than the pixels on your monitor - so you won't see them. There are 265 cells in the smallest grey cells you see on the screen.
5. Use your scroll button or +- buttons to zoom in. At resolution 40 the cells are 2 mm apart.
6. You can populate the cells with almost any conventional georeferenced imagery, vectors or terrain. Just drop the file from your windows exporer into the library on the left of the screen. Its a P2P system so you can also publish your data to others.
If there is anyone interested in further information I suggest contacting us at our office 1-877-389-6619 or see website and I can have one of our engineers provide you with more.
Hope that helps out and appreciate your interest.
Regards, Perry
bonafide11
Worker
Umm... Can someone translate that for me? Can you make a spherical earth map for Civ, or not?
The PYXIS hexagonal grid covers the entire Earth with hexagons and 12 pentagons - starting at Res 0 with 32 cells - down infinitesimally - for example at Res 29 there are 500,000,000 hexagonal cells + 12 pentagons a meter apart. The cells are all equal area except the pentagons are 5/6 the area of a hex. There are individual cell addresses and movement rules. Imagery, terrain and vectors can populate the cells quickly. There is a tile of cells that facilitates caching and transmitting data. The cell addresses are hierarchical so that you can aggregate and decompose information from one resolution to another in a database fashion.
Rendering each pixel as a hexagon cell is probably overkill for a game or at least several generation beyond what is out there now for a game. However, it would work.
Here is mid res sample with the lower res hex grid showing as an example. Note again that the actual pixels of the imagery are hexagonal providing the high fidelity environment of multi-sources of Earth observations to make up the scene.
Perry
